Existence And Uniqueness Of Solutions Of A Kind Of Partial Differential Equations With Nonlinear Boundary Conditions

Partial differential equation is an important bridge between mathematics theory and actual application. The research on partial differential equation based on problem in physics or mechanics and so on, is not only a most important content of traditional applied mathematics but also a significant portion of modern mathematics. With the research progressing, to some problem that can be approximately solved formerly with linear partial differential equation, we must consider the effect of nonlinear factor now. So, the study on partial differential equation focuses on nonlinear partial differential equation. The qualitative analysis to nonlinear partial differential equation is very difficult, and it is a big trouble to deal it in a common way, just as linear equations. When study them, we are apt to combine relevant actual model tightly.In recent years, the qualitative study on nonlinear qualitative partial differential equation mainly focuses on the existence of partial solutions (global solutions don't exist perhaps), the existence of global solutions, regularity and the estimation on the energy decrease. But these researches mainly based on the condition of linear boundary, rarely on the condition of...